References - Bogoliubov Laboratory of Theoretical Physics - JINR

SPIN CONTROL BY RF FIELDS AT ACCELERATORS AND STORAGE
RINGS
Yu. M. Shatunov
Budker Institute of Nuclear Physics, Novosibirsk, Russia
Abstract
The first experiments to apply RF fields for resonant beam depolarization and
spin flip at the VEPP-2M storage ring were carried out more than 30 years ago [1].
Later this technique was used at VEPP-2M in the experiment for comparison of
electron and positron anomalous magnetic moments. Recently, interest in RF spin
control has appeared at proton machines. This paper describes a general approach
for consideration of RF influence on spin dynamics at electron (positron) and hadron
accelerators. Some practical applications of RF fields are discussed.
The spin motion of a particle in electromagnetic fields is described by the BMT equation:
[2]
−Ω =
� q0
γ
+ q′
�
dS
dt = ˙ S = [Ω × S]
γ B�
� �
q0
+ + q′ [E × V] , (1)
γ +1
B⊥ + q0 + q ′
where q0 and q ′ are normal and anomalous parts of the particle gyro-magnetic ratio;
B⊥ and B� are magnetic field components along and transverse to the particle velocity
V. Since in circular accelerators the one-turn energy change is relatively small, we can
neglect, in the first approximation, the electric field: E =0. Following the usual approach
for orbital motion, we use as the independent variable the generalized azimuth θ and
subdivide the spin precession vector in two parts: Ω = W0(θ) +w(θ), where W0(θ)
contains only fields on the Closed Orbit R0, while w(θ) denotes all of the other terms
(contributions from closed orbit imperfection and orbital oscillations). One can treat
w as a small perturbation for the spin motion.( [3]- [5]) In the accelerator vector triad
ex, ey = V/V, ez =[ex × ey] components of the precession vector W0 can be presented
in the linear approximation in the next form: 1
W0x = ν0Kx; Kx = Bx
;
B0
W0y = (1+a) Ky; Ky = By
;
B0
W0z = ν0Kz; Kz = Bz
, (2)
where we introduce the particle magnetic anomaly a = q ′ /q0 and denote ν0 = γ · a. On
the reference orbit the equation has one solution n0, which is periodic around the ring,
1 We use dimensionless units: fields are normalized to mean guiding field B0 =1/2π � Bzdθ; length
and time are measured correspondent in units of mean radius R and revolution time.
431
B0